  ### Home > INT1 > Chapter A > Lesson A.1.6 > ProblemA-66

A-66.

Examine the pattern of tiles below.

 tile $\space$ tile $\space$ tile $\space$ tile $\space$

Figure 1

 tile $\space$ tile $\space$ tile $\space$ tile $\space$ tile $\space$ tile $\space$ tile $\space$ tile $\space$ tile $\space$

Figure 2

 tile $\space$ tile $\space$ tile $\space$ tile $\space$ tile $\space$ tile $\space$ tile $\space$ tile $\space$ tile $\space$ tile $\space$ tile $\space$ tile $\space$ tile $\space$ tile $\space$ tile $\space$ tile $\space$

Figure 3

1. On graph paper, draw Figures 4 and 5.

Figure 1 is a $2$-by-$2$ square.
Figure 2 is a $3$-by-$3$ square.
Figure 3 is a $4$-by-$4$ square.
That means Figure x should be a $(x + 1)-\text{by}-(x + 1)$ square.

2. What would Figure 10 look like? How many tiles would it have on each side? What about Figure 100?

Refer to part (a).

Figure 10: An $11$-by-$11$ square that would have $121$ tiles.
Can you use the pattern to find what Figure 100 would look like?

1. Cami has a different pattern. She decided to represent the number of tiles in her pattern in a table, as shown below. Can you use the table to predict how many tiles would be in Figure 5 of her tile pattern? How many tiles would Figure 8 have? Explain how you know.

 Figure Number $1$ $2$ $3$ $4$ Number of Tiles $5$ $9$ $13$ $17$
• Find the pattern in the chart.